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Helmholtz 3D

This is the most geometrically complex example in the tutorial set: a 3D Helmholtz problem on an extruded letter-F style geometry.

Problem Setup

The script works with mixed boundary conditions on a 3D domain and compares VPINN and FEM-style weak-form ideas on a nontrivial mesh.

Step 1: Build a Custom 3D Geometry

A custom geometry constructor creates the volume and tagged surfaces required for boundary conditions.

Step 2: Assemble Weak-Form Quantities in 3D

The example uses tetrahedral-style weak-form machinery rather than a pointwise PDE residual.

Step 3: Visualize the 3D Result

The script includes a surface or boundary visualization pipeline so the final field can be interpreted geometrically.

What To Notice

  • This is a high-end tutorial example rather than a first learning example.
  • Complex geometry handling is one of the main reasons weak-form approaches become valuable.
  • The workflow shows how jNO scales beyond unit-interval and unit-square toy problems.

Script Snippet